Managers aren’t responsible for what staff do. Staff are responsible for what staff do. If people aren’t responsible for what they do, then they don’t do what they do responsibly.
The idea that managers are responsible for staff actions is an attribute of organisations where staff are controlled, where there is a system of control.
When staff know their job and do it their way they are also responsible for their job. It is when managers that are controllers intervene to control the way staff do their job that the responsibility of staff for their job, and the ability of staff to do their job, is compromised. Manager-controllers have full responsibility for that mistake.